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 A295847 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s. 8

%I

%S 1,2,2,4,11,4,7,29,29,7,12,80,104,80,12,21,261,467,467,261,21,37,789,

%T 2197,3472,2197,789,37,65,2354,9645,26544,26544,9645,2354,65,114,7199,

%U 43335,190943,333366,190943,43335,7199,114,200,21889,195508,1406191

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.

%C Table starts

%C ...1.....2......4........7.........12...........21.............37

%C ...2....11.....29.......80........261..........789...........2354

%C ...4....29....104......467.......2197.........9645..........43335

%C ...7....80....467.....3472......26544.......190943........1406191

%C ..12...261...2197....26544.....333366......3804661.......45214991

%C ..21...789...9645...190943....3804661.....68406015.....1296880337

%C ..37..2354..43335..1406191...45214991...1296880337....39611268638

%C ..65..7199.195508.10368395..538013975..24467737897..1200659717965

%C .114.21889.876170.76065766.6343699611.457692634063.36061398110075

%H R. H. Hardin, <a href="/A295847/b295847.txt">Table of n, a(n) for n = 1..311</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)

%F k=2: a(n) = 3*a(n-1) -a(n-2) +6*a(n-3) -8*a(n-4)

%F k=3: [order 9]

%F k=4: [order 16]

%F k=5: [order 35]

%F k=6: [order 73]

%e Some solutions for n=4 k=4

%e ..1..0..0..0. .1..1..1..0. .0..1..0..0. .0..0..1..1. .0..1..1..0

%e ..1..0..1..1. .0..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..1

%e ..1..0..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..1..0..0

%e ..1..0..0..0. .0..0..0..1. .0..0..1..0. .1..0..1..1. .0..1..0..0

%Y Column 1 is A005251(n+2).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Nov 29 2017

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Last modified May 23 07:54 EDT 2022. Contains 353961 sequences. (Running on oeis4.)